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1Semiconductor Devices forQuantum ComputingLaboratory for Physical Sciences, University of MarylandBruce KaneICPS 27 Tutorial Session #3Semiconductor Devices and Quantum ComputingJuly 25, 2004www.lps.umd.edu2Outline1.Why QC?2.Requirements for a quantum computer3.Picking a good qubit (charge, spin, etc.)4.Picking the right materials (silicon, GaAs, etc.)5.Proposals for QC in semiconductors6.Recent Experimental work7.Picking the right interactions between qubits8.Prognosis: The formidable obstacles to scalingand the need to develop atom-scale devices3Computer Science in a NutshellThere are two types of problems in the world:Easy & Hard4Solutions to easy problems can be found ina number of steps that is a polynomialfunction of the size of the input.Example: Multiplication8×5=4078×45=5×8+5×70+40×8+40×70=3510Multiplication of digits of length n requiresn2 references to a times table5Solutions to hard problems can be found in anumber of steps that is a exponential function of thesize of the input.Example: Traveling Salesman Problem:1

23 41→2→3→4→1 : Bad1→3→4→2→1 : GoodNumber of possible routes goes as (n-1)!, wherenisthe number of cities visited.15 cities: 1011routes30 cities: 1031 routes6Is a problem that is hard on one computerhard on allcomputers?

Yes, if the differences are in software(Windows v. Linux v. Mac).

What if the difference is hardware?

Ultimately, the process of computation mustbe a physical process, and the questioncannot be answered without reference tophysics.7Feynman first noted that the problem of simulating a quantummechanical system is hard in the computer science sense:Consider a system of spin ½ particles:The number of terms needed to determine the wave function grows Exponentially with the number of spins:1 spin: Ψ=α1|0> +α2|1>2 spins: Ψ=α1|00> +α2|01> +α3|10> +α4|11>3 spins: Ψ=α1|000> +α2|001> +α3|010> +α4|011> +α5|100> +α6|101> +α7|110> +α8|111>A quantum system “doing what comes naturally” is performing acalculation which is exponentially hard to emulate on a classicalcomputer.Note: for 1000 spins Ψ contains 21000≈10300 terms!8Can a quantum mechanical system “doing whatcomes naturally” be used to solve any other hardproblems?Answer (Peter Shor, 1994): Yes!This result has spurred tremendous interest inthe development of a “quantum computer”.9Shor’s algorithm determines the prime factors of large compositenumbers.15=3×5221=13×17RSA-200 =27997833911221327870829467638722601621070446786955428537560009929326128400107609345671052955360856061822351910951365788637105954482006576775098580557613579098734950144178863178946295187237869221823983 = ?× ?Public key cryptography relies on the difficulty of this problem.Classical computation time is exponential in the number of digits.A quantum computer using Shor’s algorithm can factor in a number ofsteps quadratic in the number of digits.→A PC-sized quantum computer could compromise the security of allpublic key cryptography data (internet, bank transactions, etc.)10Quantum LogicClassicalQuantumComputer Computer0,1 |0>,|1>Bits"Qubits":Quantum state ofa two level systemsuch as spin 1/211Important Differences between quantum andconventional computers:

12Why quantum computation is so difficultEven ifmeasurements of single quantum states can be made reliably:♦quantum phase is a continuous variable and errors will be cumulative(like analog computer).♦Quantum systems inevitably interact with their surroundingenvironment, leading to the destruction of the coherent state upon whicquantum algorithms rely.Quantum computation ruined by decoherence unless errors can becorrected.Consensus until 1995: thinking about quantum computationis entirely an academic exercise.13Quantum error correction, discovered in the late 1990’smeans that ‘perfect’ quantum computation can beperformed despite errors and imperfections in the computer.Accuracy thresholdfor continuous quantumcomputation≈1 error every 10,000 steps.Consensus in today: building a quantum computer may stillbe a difficult (or impossible) enterprise, but the issue can onlybe resolved by doing experiments on real systems that maybe capable of doing quantum computation.14Things necessary for a spin quantum computer:1. Long lived spin states2. Single spin operations (Q NOT)controlled spin interactions with an external field 3. Two spin operations (Q CNOT)controlled interactions between spins4. Single spin preparation and detectioncontrolled interactions with external reservoirs15Grand Challenge Quantum Computing Poses to Physicists andEngineers:1. Identify systems in which single quantum states (qubits) maybe accurately measured and manipulated.2. Learn to control interactions between quantum states in acomplex, many-qubit system.Note: State of the art for solid state quantum computing~2 qubitsWhat we need for Shor’salgorithm~10,000 qubits16QC implementation proposalsOptical QCBulk spinresonance QCAtom QCSolid State QCLinear OpticsCavity QEDTrapped IonsOptical LatticesSuperconductorsSemiconductorsElectrons on heliumFluxQubitsChargeQubitsOrbital statequbitsElectron spinqubitsNuclear spinqubits17PhotosTop: IBMBottom: TU DelftGood news: Semiconductor fabrication technology isadvancing at a rapid rate.18Bad News: In semiconductors many quantum degreesof freedom are present, and all tend to interact with eachother.Semiconductor qubits maydecohererapidly.Many quantum logic operations must be performedon a qubit before decoherence occurs.1910-3sec.10-6sec.10-9sec.10-12sec.10-15sec.1 sec.Electron orbitalstatesControlDephasingElectron spinstatesControlDephasingNuclear spinstatesControlDephasing?FastMicroprocessorWe would like tdephasing/ tcontrol≥10420Spin qubits•Qubit stored on a singleelectron or nuclearspin•Extremely well isolated and localized•Quantum transport via electrons (or photonsover the long haul)•Rapid logic and measurement operationspossible in principle•But devices must be engineered at or nearthe atomic level21Decoherence times of spins inevitably will depend on whatmaterials they are situated in.22III-V’s:no stable isotopeswith nuclear spin =0IV,VI: stable isotopeswith nuclear spin=0 and≠0Spin-orbitinteractionincreases withlarger atomicnumber23QC Models24Experimental Focus of Current Research:What are decoherence times and mechanismsin semiconductor materials?Development and demonstration of single spinmeasurement devicesWe’ll look at recent work in Si, diamond and GaAs25In Si:P at Temperature (T)=1K:electron relaxation time (T1) = 1 hourG. Feherc. 1956(ENDOR)2627Use confocalmicroscopeto focus on a single NVcenter28quant-ph/04020872930Quantum LogicQuantum logical devices will have to control the interactionof single spins with their environment and with their neighborswith extraordinary precision.31Spin interactions in a semiconductorElectron spinexchange interactionElectron spindipolar interactionNuclear spindipolar interactionElectron-nuclearhyperfine interactionInteractionExtentStrength32rBµ32rNµContactSize ofWave function10 kHz (100 Å)10 mHz(100 Å)10 MHz-1 GHz(donors)>> 1 GHzAnisotropic ExchangeLarge in somematerials32Exchange InteractionWell suited to implementing quantum logic via√SWAP3334It will be difficult to know the exchange interactionspins in quantum dots with any precision.This problem can be even worse in silicon because ofits band structure.35Wellardet al. Phys. Rev. B 68 195209 (2003).36One way out: Use hyperfine coupling instead of Exchange→|↑a)~ 30 Å (in Si)e- (S=½): 31P+ (I=½)|4〉〉〉〉H=A I∙SIn unstrained pure Si, A=117.53±0.02 MHz (Feher)Electron-nuclear interaction is very close to pure Heisenberg,probably better than for two electrons.37Status of Semiconductor QC•Single spin manipulation and measurement,while difficult, appear to be in reach.•But can will large scale quantum computingbe possible?38Most Technologies aren’t scaleable!19581970Today39Imperatives of large-scale QC•Parallel operations(measurement and logic)•Efficient quantum information transport•Manageable classical control, preferablyfacilitated by nearly identical devices40Scaling and Classical Control•In most proposed quantum computerarchitectures, quantum logic andmeasurement are performed using classicallogic circuitry to control gate voltages, laserpulses, or other means used to determine thequantum state of the system. Does thecomplexity of this classical control “blowup” as the size of the quantum computerincreases?41SIMD = "single instruction, multiple data"= No!42V12(t)V23(t)V34(t)V45(t)V56(t)V67(t)V78(t)Control of a “SWAP Wire” using applied gate voltagesA tremendousincrease in scaling efficiency would result if single controllines could control multiple gates.43Making “identical devices” for scaling is much harder forQC than it is for CC.Intel Corp.44•Single donor devices (Australian QC group and many othersworking hard on this)•Single atoms and molecules attached to semiconductor surfaces?The materials science and nanofabrication communities needto start thinking about “monoclonal” (i.e. atomicallyidentical) devices and how to implement them45“Bottom up” NanofabricationSingle atom Manipulationusing an STM.(M. Crommieet al.)Taken from “Silicon-basedmolecular electronics” S.Dattaet al.Schofield et al.: PRL91 136104 (2003).46•For future devices it would be desirable tocouple surface atoms and molecules toconducting electrons within a siliconcrystal.47Electron system on a hydrogenpassivated silicon surfaceE+-[Q5.126] Electron Transport on Hydrogen-Passivated Silicon SurfacesKevin Eng, Robert McFarland, Bruce Kane48Conclusions1.QC has the potential to revolutionize the way we solve a limitednumber of problems2.Semiconductor QC implementations have important advantages(existing technological base, vast research effort innanofabrication ) and disadvantages (decoherence) compared toalternatives3.Devices demonstrating single electron spin manipulation andmeasurement are difficult, but doable4.Nonetheless, there are very serious doubts about the ability toscale simple quantum logical devices into a technologicallyrelevant quantum computer5.This (mildly) pessimistic outlook presents new opportunities forsemiconductor physics research and nanofabrication at the endpoint of Moore’s Law scaling.